1) Neutrino Background Radiation due to Supernove ExplosionRecently Superkamiokande project has started and it can observe the relic neutrino through supernove explostion. We investigated carefuly the spectrum of relic neutrino using the model for the chemical evolution of galaxies. The total flux depends strongly on the Hubble parameter, but weakly on the cosmological constant. We found that in the same flat universe model the flux in lambda=0 is smaller than that in lambda*o.2) Primordial NucleosynthesisThe primordial nucleosynthesis is best tool for deciding the baryon density. Recently, associated with the progress of techonology in obsevational field, the obsevational result pointed out that the simple model for cosmology has a trouble point. Some of people call the problem as 'crisis' in the universe. Hence, we taken account of the theoretical error in the lepton asymmetry universe and estimeted statistically the final fraction of the light elements by Monte Calro simulation. The result is that the best values for the degenerate parameter and the baryon density are 0.043(]SY.+-。[)0.040 and 0.015(]SY.+-。[)0.006-0.003 (CL.95 percent).